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Uncertainty Quantification for Inferring Hawkes Networks
Haoyun Wang · Liyan Xie · Alex Cuozzo · Simon Mak · Yao Xie

Thu Dec 10 09:00 AM -- 11:00 AM (PST) @ Poster Session 5 #1440

Multivariate Hawkes processes are commonly used to model streaming networked event data in a wide variety of applications. However, it remains a challenge to extract reliable inference from complex datasets with uncertainty quantification. Aiming towards this, we develop a statistical inference framework to learn causal relationships between nodes from networked data, where the underlying directed graph implies Granger causality. We provide uncertainty quantification for the maximum likelihood estimate of the network multivariate Hawkes process by providing a non-asymptotic confidence set. The main technique is based on the concentration inequalities of continuous-time martingales. We compare our method to the previously-derived asymptotic Hawkes process confidence interval, and demonstrate the strengths of our method in an application to neuronal connectivity reconstruction.

Author Information

Haoyun Wang (Georgia Tech)
Liyan Xie (Georgia Institute of Technology)
Alex Cuozzo (Duke University)
Simon Mak (Duke University)
Yao Xie (Georgia Institute of Technology)

Yao Xie is an Assistant Professor and Harold R. and Mary Anne Nash Early Career Professor in the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, which she joined in 2013. She received her Ph.D. in Electrical Engineering (minor in Mathematics) from Stanford University in 2011, M.Sc. in Electrical and Computer Engineering from the University of Florida, and B.Sc. in Electrical Engineering and Computer Science from University of Science and Technology of China (USTC) . From 2012 to 2013, she was a Research Scientist at Duke University. Her research areas include statistics, signal processing, and machine learning, in providing theoretical foundation as well as developing computationally efficient and statistically powerful algorithms for big data in various applications such as sensor networks, imaging, and crime data analysis. She received the National Science Foundation CAREER Award in 2017 and her crime data analytics project received the Smart 50 Award at the Smart Cities Connect Conferences and Expo in 2018.

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